A New Approach to Correspondence Analysis Based on Interval-Valued Hesitant Fuzzy Sets

Correspondence Analysis (CA), a multivariate statistical technique, allows a visual representation of the association between categorical variables through a contingency table consisting of frequencies representing the existence of relationships. Despite being a widely used statistical technique, the classical CA is not able to demonstrate the uncertainty in real-life problems. To address this issue, a new Interval-valued Hesitant Fuzzy CA approach is proposed to represent the uncertainty caused by human doubt. Due to the nature of operations defined on Hesitant Fuzzy Sets, it is hard to integrate the fuzzy calculations directly into the classical CA. Thus, a new hesitant expected value method is proposed to reveal the independence between two categorical variables. As the output of the proposed approach, an interval-valued hesitant fuzzy correspondence map consisting of rectangles of different sizes representing the amount of the hesitancy is constructed. The applicability of the proposed approach is demonstrated by a simple but effective illustrative example.